Transfer tomato mixture to a blender. Cover and hold lid down; pulse a few times before leaving on to blend. Puree in batches until smooth. Transfer tomato puree back to pressure cooker.

Stir chicken stock into tomato puree; cook and stir over high heat until just boiling, about 5 minutes. Cover and lock pressure cooker. Cook over high heat until steam begins to build and steadily escapes. Lower heat to medium-low; cook for 20 more minutes. Remove from heat; allow all the steam to naturally release. Remove lid.

Bring soup to a boil; stir in cream and cilantro. Remove from heat. Let cool for 5 minutes.